Physics and math textbooks for self study

[Happiness]

Is there a one-stop textbook for physics major students, a single book that teaches you the required math for a particular physics subtopic before teaching you the physics (or teaches you both the math and physics together)? I find standard undergraduate textbooks, such as Classical Mechanics by Goldstein, Poole and Safko, difficult to use for self study.

It would be better imho if
1. certain/most mathematical steps are explained in more detail or with more emphasis
2. exercises are grouped according to sections instead of being one whole chunk at the back of the chapter as this would require the reader to finish the whole chapter before he could do any exercises
3. more worked examples in the main text (these fortunately are present in Introduction to Electrodynamics by David J. Griffiths)
4. include only the essential materials or have some labels to distinguish essential materials from non-essential ones so that readers can get familiar with a topic as fast as possible and they can later choose to read the non-essential materials if they want to go more in depth

The book's content page may look like this:
1. Basic algebra and calculus
2. Basic classical mechanics
3. Probability 1
4. Statistical mechanics 1
5. Linear algebra 1
6. Quantum mechanics 1
7. Vector calculus
8. Electromagnetism 1
9. Calculus 1
10. Classical mechanics 1

The book then gradually guides the readers to more advanced levels.

Suppose I plan to study quantum mechanics for a month. If I study a textbook chapter by chapter, I may get familiar with one or two chapters, which means I would become very well versed in certain aspects of quantum mechanics but have very poor knowledge on other aspects. For example, if the chapter I read is on angular momentum, I would be very good, say, in calculating Clebsch-Gordan coefficients, but have no idea on any approximation methods and perturbation theory. My point is Clebsch-Gordan coefficients are very technical and studying a textbook chapter by chapter (because of the way most textbooks are structured) would bring me too deep into one aspect at the expense of the overall big picture. I would rather gain an understanding of everything in less depth from wave-particle duality to hermitian operators to many-particle systems to EPR paradox.

 

[Mondayman]

I find standard undergraduate textbooks, such as Classical Mechanics by Goldstein, Poole and Safko, difficult to use for self study.

That's because it is a standard grad level textbook. Try An Intro to Mechanics by Kleppner/Kolenkow, or Classical Mechanics by Taylor.

But seriously, a textbook that covered everything from basic algebra to quantum mechanics would be as heavy as my granite countertop! I highly doubt such a book exists.

 

[Happiness]

That's because it is a standard grad level textbook.

It's one of the recommended textbooks for MIT undergraduate classical-mechanics courses. I thought that means it's an undergraduate-level textbook. No?

 

[Mondayman]

That's at MIT. I'm sure there are other schools that recommend it as well. But it is most typically used at the graduate level.

 

[jtbell]

MIT is not a typical undergraduate institution.